Finite Group Databasebeta

← Prev (#38737359) Next (#38737361) →

C23×#11763981 #38737360

order25116
automorphism?
homologyAbelianization (H1) = C3×C4×C23 · Schur multiplier (H2) = C1

Aliases

direct productC23×#11763981

Splittings

Fitting, socle, HallC7×C13×C23 ⋊ C3×C4
derived, HallC7×C13 ⋊ C3×C4×C23
HallC7×C23×#261 ⋊ C3
HallC23×#63271 ⋊ C4
HallC23×#261 ⋊ ΓL(1,𝔽8)
HallC7×#261 ⋊ C3×C23
HallC13×C23 ⋊ C4×ΓL(1,𝔽8)
Hall#63271 ⋊ C4×C23
HallC7×C23 ⋊ AGL(1,𝔽13)
Hall#261 ⋊ ΓL(1,𝔽8)×C23
SylowC13 ⋊ C4×ΓL(1,𝔽8)×C23
SylowC7 ⋊ C23×AGL(1,𝔽13)

Subgroups

subgroupG/H
center, hypercenterC23#11763981
commutator, hypocenterC7×C13C3×C4×C23
FrattiniC1G
Fitting, socleC7×C13×C23C3×C4
prime radicalC23×#10587717C2
cosocleC7×D13C2×C3×C23
LCSG ▷ C7×C13
UCSC1 ◁ C23

48 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 2093

Conjugacy classes & character table

621 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(25116, 79);